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SERI/TP-252-2952UC Category: 59aPreprintDEB6014502
Moisture Transport in.Silica Gel Packed BedsII. Experimental Study
Ahmad A. Pesaran (SERI)Anthony F. Mills (University of Californ ia)
August 1986
To Appear inInternational Journal ofHeat and Mass Transfer
Prepared under Task No. 3022.210FTP No. 01-540
Solar Energy Research InstituteA Division of Midwest Research Institute
1617 Cole BoulevardGo lden, Colorado 80401-3393
Prepared for the
U.S. Department of EnergyContract No. DE-AC02-83CH10093
NOTICE
This report was prepared as an account of work sponsored by the United StatesGovernment. Neither the United States nor the United States Department of Energy,nor any of their employees. nor any of their contractors. subcontractors, or theiremployees, makes any warranty, express or implied. or assumes any legal liabilityor responsibility for the accuracy, completeness or usefulness of any information,apparatus, product or process cisclosec. or represents that its use would notinfringe privately owned rights.
, .
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TP-2952
MOISTURE TRANSPORT IN SILICA GEL PACKED BEDS
II. EXPERIMENTAL STUDY
Ahmad A. Pesaran* Anthony F. Mills
Solar Energy Res~arch Institute School of Engineering and Applied Science
Golden, CO 80401, USA
ABSTRACT
University of California
Los Angeles, CA 90024, USA
Experiments have been performed to obtain the transient response of a thin
adiabatic packed bed of silica gel after a step change in inlet air condi-
t i ons , Comparisons are made with predictions using a solid-side resistance
model and a pseudo-gas-side controlled model and better agreement obtained
with the former model. An apparent dynamic hysteresis for adsorption!
desorption with microporous silica gel is clearly in evidence, which could be
due to solid side effective diffusion coefficient which decreases with
increasing moisture content, or to a lesser extent to a hysteresis in the
adsorption isotherm itself.
*At the School of Engineering and Applied Science, UCLA during the course ofthis work.
1
a
A
NOMENCLATURE
average pore radius
cross section area of bed
specific heat of liquid water
constant pressure specific heat of humid air
constant pressure specific heat of water vapor
desiccant to air ratio, PbAL/mGT (dimensionless)
TP-2952
D
D*
ID
total diffusivity, defined by Eq. 13
DT/R2 (dimensionless)
Knudsen diffusion coefficient
surface diffusion coefficient
equilibrium isotherm, pml' = g (W,T)
derivative of equilibrium isotherm, g'(W) = p(aml/aW)T
convective heat transer coefficient
heat of adsorption
Intermediate Density (macroporous)
gas-side mass transfer coefficient
effective mass transfer coefficient
length of bed
water vapor mass fraction (kg water/kg humid air)
2
NOMENCLATURE (Continued)
me mass flow rate of gas mixture
TP-2952
Nt u number of transfer units, KG L/mG or KC,eff Lime (dimensionless)
P pressure
PGC pseudo-gas-side controlled
p perimeter of bed
r radial coordinate in a particle
r* r/R (dimensionless)
R particle radius
R H20 gas constant
Re Reynolds number, 2RV/~ (dimensionless)
RD Regular Density (microporous)
RH relative humidity, P1/psa t (dimensionless)
SSR solid-side resistance
t time
t* dimensionless time, tiT (dimensionless)
T temperature
V superficial velocity of alr
W desiccant water content (kg water/kg dry desiccant)
z axial distance
z* z/L (dimensionless)
Greek
6 ppD/KGR (dimensionless)
porosity (dimensionless)
3
NOMENCLATURE (Concluded)
v kinematic viscosity
TP-2952
p density of humid air
Pp particle density
, duration of experimental run
'g tortousity factor for intraparticle gas diffusion (dimensionless)
's tortousity factor for intraparticle surface diffusion (dimensionless)
Subscripts
1 water vapor
2 dry air
avg average value
b bed; bulk
e surrounding humid air
eff effective value
K Knudsen diffusion
tn inlet value
o initial value
out outlet value
p particle
S surface diffusion
s s-surface, in gas phase adjacent to gel particles, or dry solid phase
of the bed
sat saturation
4
TP-2952
1.0 INTRODUCTION
Part I of this series [1] reported an analytical study of the transient
response of thin silica gel packed beds to a step change in inlet air humidity
or temperature. Special attention was given to moisture transport within the
silica gel particles since earlier investigators [2,3,4] showed that the
solid-side moisture transfer resistance is generally larger than the gas-side
resistance. A model which accounts for both Knudson and surface diffusion of
moisture within the particles was proposed and incorporated into a simul
taneous heat and mass transfer model for predicting the transient response of
thin silica gel packed beds. The model is called the Solid Side Resistance
(SSR) model and includes both solid- and gas-side resistances. The predic
tions of the SSR model were compared with predictions of the widely used
Pseudo-Gas-side Controlled (PGC) model. In the PGC model the overall mass
transfer from the air stream to the silica gel is represented by a gas-side
coefficient which is reduced to account for solid side resistance.
Part II of this .series describes an experimental program which obtained data
for the evaluation of the analytical models. A bench-scale test rig was
bui 1t , and adsorpt ion and desorpt ion experiments performed on microporous
Regular Density (RD) and macroporous Intermediate Density (10) silica gel in
adiabatic thin packed beds. Section 2 describes the experimental rig, instru
mentation, procedure, and test materials; Section 3 presents the results and a
discussion. Section 4 presents our conclusions.
5
2.1 Apparatus
2.0 EXPERIMENTAL KETHOD
TP-2952
A schematic of the experimental system is shown in Fig. 1. The system con
sists of a dryer, an air heater, a humidifier, a blower, a heat exchanger, and
a desiccant bed in a test chamber. The dryer, air heater and humidifier are
used to generate the desired inlet air conditions for the test chamber; the
a~r heater is also used to regenerate the silica gel both in the test chamber
and in the dryer.
The dryer used to provide dry air for step change experiments is a stainless
steel cylinder 0.55 m high, and 0.19 m in diameter. A packing height of
0.42 m of 3-8 mesh RD silica gel (Davison, Grade 01) is used. A computer code
[3,4,6] was used to design the dryer and for prediction of its performance.
The dryer can be isolated from the system by closing valves 2 and 4.
The a~r heater ~s used to regenerate the silica gel in both the test chamber
and the dryer. It 1S a commercial 1.5 kW electrical heater manufactured by
Pacific Chromalox. It consists of two electrical heating elements contained
in a well-insulated stainless steel casing. The outlet air temperature can be
controlled by controlling the power supplied to the heater with an AC Variac.
The humidifier for providing humid a1r for the experiments 1S a cast acrylic
cylinder 0.73 m high and 0.72 m inside diameter, packed with 1/2 inch ceram~c
Berl saddles. The height of the packing in the original design was 0.5 m,
However, after some preliminary tests the hei.ght was reduced to 0.25 m for
6
TP-2952
better control of humidity. The packing is supported by a perforated acrylic
plate. The process air enters from below and contacts with water sprayed on
top of the packing. Tap water is fed to the top of the packing. The humidi
fier can be removed from the system by closing valves 5 and 7.
Air flow is provided by a positive displacement rotary blower manufactured by
Gardner-Denver (model 2PDR) wi th a capacity range of 1.4x 10-3 to 0.1 m3/ s ,
The blower is driven by a 3 HP, 230 VAC, 3 phase induction motor, through a
belt and pulley system. The blower capacity can be changed by operating at
different shaft speeds using different pulleys, and/or by varying the rate of
air by-pass, i.e., controlling valve 1. Since the blower blows the air
through the system, all components are under a slight pressure.
The test chamber is a 0.13 m I.D. Pyrex glass cylinder with a wall thickness
of 6.5 mm , The test chamber has three sections: the main section, a top
section, and a lower section. Air enters through the top, passes through a
flow straightener of about 0.18 m height of Berl saddle packing to provide a
uniform flow before entering the silica gel bed. The uniformity of flow was
satisfactory as checked with a hot wire anemometer. The silica gel bed is
supported by a copper screen, which, in turn, 1 s supported by the lower
section of the test chamber. The height of the bed is varied by adding more
or less silica gel from the top of the test chamber. To approximate the
adiabatic operation, the test chamber is insulated wi th fiberglass during
testing.
The purpose of the heat exchanger is to cool the hot process alr after
adsorption to a dry bulb temperature in the useful range of the hygrometer
7
TP-2952
sensor used for measuring humidity. The heat exchanger consists of a copper
coil welded to an aluminum cylindrical casing. Tap water is fed to the top
of the coil and the process a i r is passed through the aluminum cylinder
cocurrently with the water. The system components are connected through
1.25 inch (0.0.) galvanized pipes and 1.5 inch rubber hose connectors. The
pipes are insulated for a better temperature control and to reduce heat loss
during regeneration.
2.2 Instrumentation
The volume flow rate 1S determined by a calibrated Rockwell Testmeter (model
No. 415). Associated air pressure and temperature measurements are made using
a mercury manometer and thermocouple, respectively, to convert volume flow
water rate to mass flow rate. A standard ASME orifice system with required
manometer calibrated the Testmeter. The expected error in measurement of air
flow rate is less than 3%.
The pressure drops across the desiccant bed, dryer and humidifier are measured
using water manometers. The air temperatures upstream (at station D) and
downstream (at station E) of the bed, outlet from the humidifier (at
station C), and outlet from dryer (at station B) are measured uSlng dry
thermocouples made from 30 gauge (0.0. = 0.25 mm) type K, chromel-alumel
wires. Chromel-alumel thermocouples were chosen because of their resistance
to corrosion in water and humid air, and also for their low conductivity so as
to reduce lead conduction errors. The dry thermocouples are provided with
radiation shields for reduction of radiation losses and the readings corrected
where appropriate. The expected error in temperature measurement is less than
a.soc.8
TP-2952
The relative humidity of the process air is measured us mg a hygrometer
manufactured by Weather Measure Corp. (Model HMS-14) with a single dielectric
polYmer sensor with a very short response time (90% of final relative humidity
in one second) • The sensor of the hygrometer can be mounted at several
locations (stations C, F and G) in the system for various purposes. At each
mounting station a thermocouple junction is provided for measurement of tem--
perature along with measurement of relative humidity so that the water vapor
concentration can be calculated. A resistance type hygrometer manufactured by
Hydrodynamics Inc. (Model 15-3001) is also used with sensors appropriate to
different humidi ty ranges. These sensors have a slower response than the
Weather Measure sensor and thus are used for measurement of uniform humidities
from the dryer or humidifier to the desiccant bed. The bed outlet humidity
measurement was corrected for time lag due to the distance between the bed
outlet and the measuring- station. The error i n measurement of relative
humidity is 3%. Considering other errors in measurement of temperature and
total pressure the estimated error in measurement of water vapor mass fraction
is less than 6%.
All thermocouple junctions are spot welded and connected to a millivolt
recorder and a cold junction compensator manufactured by Fluke Company
(model 2240A Datalogger). The voltage outputs of all the thermocouples and
the hygrometers are recorded simultaneously at a preprogrammed time interval
by the Datalogger.
9
TP-2952
2.3 Procedure
Tests were performed to determine the transient response of thin silica gel
packed beds to a step change in inlet conditions. A bed of known initial
water content and temperature was prepared using the heater of the humidifier,
and then sealed. Commencing at time t=O process air with selected constant
humidity and temperature was passed through the bed. The outlet air condi
tions (temperature and relative humidity) from the bed were measured as a
function of time and the data collected. Two types of experiments were
performed, namely, adsorption and desorption. In adsorption experiments, the
initial bed water content is lower than the equilibrium value corresponding to
the process air, i.e., Wo < W (m1,in' Tin' p). In desorption experiments, the
initial bed water content is higher than the equilibrium value corresponding
to the process air, i.e., Wo > W (m1,in' Tin' p). The experiments were termi
nated after 20-30 minutes which 1S typical of cycle times between adsorption
and desorption processes encountered in operation of dehumidifiers 1n
desiccant cooling systems. The collected data were converted to engineering
units and plotted and compared with the model predictions as shown 1n
Section 3.
2.4 Test Material
Both mic r opo rous silica gel (Regular Density, Davison Grades 01, 03, 40 and
408) and macroporous silica gel (Intermediate Density, Davison Grade 59) were
tested to investigate the effect of average pore diameter and equilibrium
isotherm on bed performance. The major difference in various grades of RD gel
is their range of particle size. It is reasonable to assume that the solid
10
TP-2952
S=~II.I
side resistances varies with gel particle size and thus a wide range of gel
sizes was tested (0.6-5 mm in diameter). Since the particle size range in
some of the grades are wide, they were sieved to obtain a narrow range of
particle size. The average pore sizes supplied by the manufacturer are 11 A
for RD gel, and 68 A for ID gel.
3.0 RESULTS AND DISCUSSION
Thirty-five tests were performed: due to space limitations only the results
of selected tests are used here to evaluate the validity of the theoretical
models. Table 1 summarizes the pertinent parameters of the tests. We have
presented 13 tests to show the results for two types of gel, adsorption and
desorption cases, various particle sizes, and initial and inlet air
conditions. The outlet air temperature and outlet water vapor mass fraction
as functions of time after a step charge 1n inlet air conditions to the bed
are shown by symbols in Figures 2 through 1S for thirteen tests. Predictions
using both the solid-side (SSR) model and the pseudo-gas-side controlled (PCC)
model are also shown in these figures by solid lines .. For convenience the
essential differences between these models are summarized in Table 2 ..
3.1 Adsorption on Regular Density Silica Gel
Figures 2 through 7 show results for adsorption tests with RD gel.. The
general trends of the curves for the experimental results and the theoretical
predictions are simi lar and are explained in Part I for their series [1] ..
Unless otherwise specified Eq.. (A-l) was used for the equilibrium isotherm and
11
Eq, (A-3) for the test of adsorption in the predictions. Eq, (A-6) was used
for the effective surface diffusion coefficient. Since the parameter Do,eff
had not been previously established for the H20- s i l i ca gel system, we
determined a suitable value by making calculations for a range at Do,eff
values and comparing predictions with experiment: Figures 3 and 4 show
typical results of such predictions. Based on a number of such comparisons a
value of Do,eff = 1.6 x 10-6 m2/s was chosen [5]. Theoretical predictions
with the SSR model were not made for tests on gel particles of 0.87 mm radius
and smaller: the large values of Nt u for these tests required a large number
of time and spatial node points to avoid numerical instability and thus the
computational cost was prohibitive.
By comparing predictions with experiments the following general observations
can be made. Predictions of ml,out using the SSR model are generally superior
to those of the PCC model, especially at small times. The initial slopes of
the ml,out curves from SSR model are steeper than those of PCC model and
usually match the experimental results. The PCC model usually underpredicts
the experimental ml,out' i.e., more water 1S adsorbed due to less mass
transfer resistance. In most of the experiments the measured Tout is within
the range of the predicted values of both SSR and PCC models; at small times
the agreement with SSR model is generally better. The SSR model tends to
predict peak values of T t which are higher than those for PCC model with theou
peaks occurring earlier.
12
TP-2952
S=~II.I
3.2 Desorption from Regular Density Gel
Fig~res 8 through 11 show results for desorption tests on RD gel. Again the
theoretical predictions using both models follow the general trend of the
experimental results. Again Eqs. A-l and A-3 are used for the equilibrium
isotherm and heat of adsorption, respectively. For the moisture diffusivity,
Eqs. (A-5 and A-8) are used, i.e., 'only surface diffusion is considered for RD
gel. Figures 12, 13, and 14 show that Do,e£f = 0.8 x 10-6 m2/s gives a better
match with experiment than the value of 1.6 x 10-6 used for the adsorpc i.on
experiments. The lower value of Do,eff increases the solid side resistance
and thus decreases the desorption rate: ml,out is overp-cedicted by both
models (even when the reduced value of Do,eff is used in the SSR mode), while
Tout is predicted satisfactorily by the SSR model, and is underpredicted by
the PGC model. The p-cediction of ml,out by the PCC model matches better than
that by the SSR model for Test 25 (Fig. 8), while the reverse is true for
Tests 29 and 30 (Figs. 9 and 10), when Do,eff = 0.8 x 10-6 m2/s is used in the
SSR model. A theoretical prediction for Test 35 (Fig. 11) using the SSR model
was not obtained owing to a prohibitive computer cost associated with the
large Nt u value. For this test the PGe model predicts Tout satisfactorily,
while m1,out is again overpredicted. The discrepancy between predictions of
the SSR and PCC models 1n Figures 8-10 is because they differ fundamentally as
can be seen from Table 2.
It is clear that there is a fundamental difference between the behavior of the
bed during adsorption and desorption. For example, the experimental responses
of an adsorption test (:fj24) and a desorption .test Ci!29) with similar bed and
flow conditions shown in Figure 12 present this difference. As discussed in
13
Part I [1],
TP-2952
the SSR model shows that there should be a difference due to
concentration dependence of DS,eff in the Sladek theory, Eq. (A-8): initial
rates of desorption should be higher than initial rates of adsorption with all
other pertinent parameters the same. However a comparison of figures shows
that exactly the opposite is true. Furthermore our comparison of predictions
with experiments has shown that solid side effective diffusion coefficients
appear to be one half of those for adsorption. The SSR model lacks an
essential feature: either there 1S a marked hysteresis in the adsorption
isotherm, or solid side effective diffusion coefficients decrease with
increasing gel moisture content W. Indeed, Kruckels [1,9] found it necessary
to include such a feature in correlating his experimental data for adsorption
on RD gels at low moisture contents, as discussed in Part I of this series.
The isotherm of RD gel usually does not show a strong hysteresis [e.g., 7 and
8]. However, decrease of solid side effective diffusion coefficient with
increasing gel moisture content is quite possible. The negative exponential
dependence of DS,eff in Eq. (A-B) is due to the decrease of heat of adsorption
with increasing moisture content and has a rational basis; hence, one must
look elsewhere for an explanation. A similar behavior (i.e., good agreement
for adsorption and poor agreement for desorption) was observed by Barlow [10]
and thus this apparent dynamic hysteresis can now be regarded as a firmly
established feature of RD silica gel behavior. Further experiments are
needed, in which the initial gel moisture content 1S varied over a wide range
so as to resolve whether the apparent dynamic hysteresis is due to a gel
moisture content dependent effective surface diffusion coefficient, or whether
there is a more fundamental difference between the adsorption and desorption
processes on a molecular scale. It should be noted than an. effective porosity
which decreases with increasing moisture content 1S not an unreasonable
explanation.14
TP-29525='1'.13.3 Adsorption on Intermediate Density Silica Gel
The resul ts for adsorption on ID gel are shown in Figures 13 through 15.
Equations A-2 and A-4 were used for the equilibrium isotherm and heat of
adsorption, respectively. For the moisture diffusivity Eqs. A-6, A-1 and A-aare used, i.e., both Knudsen and surface diffusion are considered for IO gel.
The Do,eff value used was the same as that established for adsorption on RD
gel, i.e., 1.6 x 10-6 m2/s, and a reasonable match between SSR model
predictions and experiment is obtained.
The general shapes of the Tout and ml,out curves are the same as those of RD
gel. However, since the equilibrium capacity of ID gel is much lower than
that of RD gel (as shown in Fig. A.l), the ID gel bed loses its adsorption
capacity faster. Thus, ml,out increases very rapidly initially and then there
is a smooth transition to a more gradual increase; Tout also increases to its
peak value very quickly, and subsequently decreases rapidly to the inlet alr
temperature. The predictions of m1,out of SSR model is better than those of
PCC model, especially at small times. This behavior is similar to that noted
before for adsorption experiments on RD gel. At longer times, ml,out is
overpredicted by SSR model. Usually, the PCC model underpredicts the experi-
mental initially and overpredicts later. 1S generally
underpredicted by both models, especially after the peak value is reached,
with PCC model doing somewhat better than SSR model.
15
TP-2952
4.0 CONCLUSIONS
1. Reasonable agreement between prediction and experiment for RO gels is
possible with both the solid-side resistance (SSR) model and the pseudo
gas-side controlled (PCC) model, though in general the SSR model gives the
better agreement.
2. The effective surface diffusion coefficient 1n the SSR model required to
match desorption data for RO gels is about one half of that required to
match adsorption data for RO and 10 gels.
3. There is an apparent dynamic hysteresis for adsorption/desorption with RO
gel, which could be due a solid-side effective diffusion coefficient which
decreases with in~reasing moisture content; a less likely possibility is a
hysteresis in the adsorption isotherm itself.
4. Further experiments, in which the initial moisture content of the gel is
varied over a wide range, are required to clarify the cause of the
apparent hysteresis.
16
TP-2952
ACKNOWLEDGMENTS
This work was supported by a grant from the Solar Energy Research Institute/
U.S. Department of Energy, Grant No. DE-FG02-80CS84056. The Technical Monitor
was T. Penney. Computer time was supplied by the Campus Computing Network of
the University of California, Los Angeles. The Publication Development Branch
of the Solar Energy Research Institute assisted in preparing this paper.
17
TP-2952
S - !!!!tl ,~=~ I~~I
REFERENCES
1. Pesaran, A. A. and A. F. Mills, Moisture Transport in Silica Gel Packed
Particle Beds 1. Theoretical Study, Intemational Journal of Heat and Mass
Transfer, in press.
2. Clark, J. E., "Design and Construction of Thin, Adiabatic Desiccant Beds
with Solar Air Condi tioning Applications," M. S. Thesi s , School of
Engineering and Applied Science, University of California, Los Angeles
(1979).
3. Clark, J. E., A. F. Mills and H. Buchberg, Design and Testing of Thin
Adiabatic Desiccant Beds for Solar Air Conditioning Applications, J. Solar
Energy Engineering, 103, (May 1981).
4. Pesaran, A. A., "Air Dehumidification i n Packed Silica Gel Beds,"
M. S. Thesis, School of Engineering and Applied Science, University of
California, Los Angeles (1980).
5. Pesaran, A. A., "Moisture Transport i n Silica Gel Particle Beds," Ph.D.
Dissertation, School of Engineering and Applied Sciences, University of
California, Los Angeles (1983).
6. Nienberg, J. W. "Modeling of Desiccant Performance for Solar Desiccant-
Evaporative Cooling Systems," M. S. Thesis, School of Engineering and
Applied Science, University of California, Los Angeles (1977).
18
TP-2952
7. W. R. Grace and Co., Davison Silica Gel, Bulletin No. lC-15-378; and
W. R. Grace and Co., Fluid Processing Handbook, Baltimore, Maryland (1966).
8. Jury, s. H. and H. R. Edwards, The Silica Gel Water Vapor Sorption Therm;
Can. J. Chern. Engr. 49, 663-666 (October 1979).
9. Kruckels, W. W., On Gradient Dependent Diffusivity, Chern. Engs. Sci., 28,
1565-1576 (1973).
10. Barlow, R. S., Analysis of Adsorption Process and of Desiccant Cooling
Systems--A Pseudo-Steady-State Model for Coupled Heat and Mass Transfer,
SERI/TR-631-1329 , Solar Energy Research Institute, Golden, CO, USA (1982).
19
TP-2952
APPENDIX A. AUXILIARY DATA
Beside the information already given for KG and hc and in Table 2, data are
required for specific heats cp,e' cpl' and cb' heat of adsorption and
equil i brium isotherm relation, and bed density, silical gel density and
diffusivities. The specific heats are assumed to be independent of
temperature which is a reasonable assumption for the range of temperature
encountered for the application of this work, namely, solar desiccant cooling
systems.
The specific heats are:
cpl = 1884 J/kg K
Cp,e = C m + c (l-ml )pI l,e p2 ,e = 1884 m1 + 1005 (1-m1 ),e ,e
J/kg K
cb = ci Wavg + csilica gel = 4178 Wavg + 921 J/kg K
Equilibrium isotherms were obtained by fitting fourth degree polynomials to
the manufacturer's data [9] for Regular Density (Davison, Grades 01, 03 and
40) and Intermediate Density (Davison, Grade 59) silica gels.
RH = 0.0078 - 0.05759W + 24.16554 W2 - 124.478 W3 + 204.226 W4
and for ID gel,
20
(A-I)
TP-2952
S=~II.1RH = 1.235 W + 267.99 W2 - 3170.7 W3 + 10087.16 W4 W ~ 0.07
RH = .3316 + 3.18 W W ::> 0.07 (A-2)
Fig. A-1 compares the equilibrium isotherm of RD and ID silica gels. The heat
of adsorption is a function of gel water content and is the summation of heat
of condensation and heat of wetting. A summary of the literature on heat of
adsorption of H20 on RD silica gel is given in [4]. A recommended correlation
that fits the available data for RD gel is
H = 3500 - 13400 Wads
Hads = 2950 - 1400 W
w ~ 0.05 IkJ/kg water
W ::> 0.05(A-3)
For heat of adsorption on IO gel no satisfactory data was found, thus the
Clausius-Clapeyron equation
was applied to the equilibrium isotherm of ID silica gel. The equilibrium
isotherm was replotted on the 1n PI versus 1/ (T + 273.15) plane, where an
approximate straight line for a constant gel water content was obtained. The
slopes of these lines gave the average heat of adsorption at each gel water
content. The following equation was fitted to the results,
H = -300 W + 2095ads
H = 2050ads
W< 0.15
w ~ 0.15
21
kJ/kg water (A-4)
TP-2952
~~-The bulk density of RD silica gel bed is 721.1 kg/m3, and that of ID silica
gel is 400.6 kg/m3• The particle density of RD silica gel is 1129 kg/m3 , and
that of ID gel is 620 kg/m3•
As discussed in Appendix A of Part I of this work [1] the total diffusivity D
depends on only surface diffusion coefficient for microporous RD gel
D = DS,eff (A-5)
and depends on both surface and Knudson diffusion coefficients for macroporous
ID gel
g'(W)D = DS eff + DK -----, Pp
where the effective diffusion coefficients are given by
(A-6)
DK eff =~ 22.86 (T + 273.15)1/2a (A-7), Tg
DS,eff = Do,eff exp [-0.947 Hads/(T + 273.15)] (A-8)
where Hads is in kJ/kg water and T in °c and a is pore size in meter. The
particle porosity (€p) and gas tortousity factor ('g) for ID gel are 0.716 and
2.0, respectively.
22
Table 1. Bed and Flow Conditions for the Experiments Ul-III~-
Test Gel Process* R L Wo To' ml,in Tin V Re Nt u1,* DAR T ItI}1"'!!~
II Type (10-3 m) (10-3 m) (oC) (oC) {m/s} (9)
1 RD AD 1.94 77.5 0.0417 23.3 0.0100 23.3 0.21 49.30 22.65 0.1285 1800
4 RD AD 1.94 75.0 0.0410 24.2 0.0105 24.2 0.32 78.60 18.74 0.0819 1800
6 RD AD 1.94 75.0 0.0450 22.1 0.0088 22.1 0.55 150.9 14.25 0.0547 1500
7 RD AD 1.27 65.0 0.0410 24.7 0.0106 24.1 0.39 10.0 26.29 0.0604 1800
21 RD AD 0.435 45.0 0.0640 20.2 0.0088 20.6 0.30 16.34 98.61 0.0554 1800
24 RD AD 2.60 50.0 0.0668 22.6 0.0109 25.6 0.40 129.8 7.62 0.0440 1800Nw
25 RD DE 2.60 50.0 0.260 25.4 0.0007 25.4 0.67 218.5 6.12 0.039 1200
29 RO DE 2.60 50.0 0.368 25.0 0.0051 23.9 0.40 131.0 7.59 0.042 1800
30 RD DE 2.60 50.0 0.370 23.8 0.0090 23.5 0.65 205.0 6.28 0.040 1200
35 RD DE 0.33 30.0 0.220 24.3 0.0008 24.3 0.28 11.32 101.1 0.040 1800
13 JD AD 1.94 17.5 0.0088 23.1 0.0097 23.6 0.45 109.41 16.85 0.050 1200
14 ID AD 1.94 71.5 0.0084 23.3 0.0074 23.3 0.18 44.0 24.70 0.0813 1860
17 10 AD 1.94 77.5 0.005 24.4 0.0063 24.4 0.67 164.19 14.21 0.033 1200
..··AD: adsorption; DE: desorption ~."I
••t ~·;1'h i s value of Nt u is for SSR model, Nt u for PGC model is about 1/3.4 of this value. t-,)\DVIt-,)
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